Why is the rate of profit not important?

I think it has to do with declining interest in Marxian economics. In the past the Marxian economics, especially the one in Sraffian tradition had much wider appeal. The rate of profit was an important metric in Marxian economics, since Marxian economics makes several important predictions about the rate of profit in 'capitalist' economies (e.g. the tendency of the rate of profit to fall (TRPF) hypothesis - see Marx Capital, Volume III).

If you look at the historical papers that discuss the rate of profit, they are very often connected to the TRPF hypothesis (although not necessarily from Marxian angle). In fact, if you just put rate of profit into google scholar now more than 1/3 of the searches relate either to Marxian economics of TRPF hypothesis. If you do the same with Palgrave dictionary of economics almost half of the results on first page are connected to Marxian economics or TRPF hypothesis. I realize this alone is not rigorous proof but it is at least bit suggestive.

In addition, I would challenge the idea that the rate of profit 'dropped from mainstream economics'. Rate of profit is often used synonymously with rate of return on capital (see Feldstein, Summers & Wachter, 1977). This is so because existence of profit is often (at least partially) attributed to the fact that firms typically own their capital, and indeed if you look at papers that try to measure rate of profit often they look at returns on assets as well such as the Feldstein et al paper above.

You will find rate of return capital to be mentioned far more often in the mainstream literature, and textbooks as well. Thus it is possible that the rate of profit was just abandoned due to the Marxist connotations.